Fundamentals of interactive computer graphics
Fundamentals of interactive computer graphics
Making the Oslo algorithm more efficient
SIAM Journal on Numerical Analysis
Generalized scanning technique for display of parametrically defined surfaces
IEEE Computer Graphics and Applications
An introduction to splines for use in computer graphics & geometric modeling
An introduction to splines for use in computer graphics & geometric modeling
The Reyes image rendering architecture
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Adaptive forward differencing for rendering curves and surfaces
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Real-time rendering of trimmed surfaces
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Rendering cubic curves and surfaces with integer adaptive forward differencing
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Ray tracing trimmed rational surface patches
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Integer forward differencing of cubic polynomials: analysis and algorithms
ACM Transactions on Graphics (TOG)
Estimating subdivision depths for rational curves and surfaces
ACM Transactions on Graphics (TOG)
Interactive display of large-scale NURBS models
I3D '95 Proceedings of the 1995 symposium on Interactive 3D graphics
Adaptive isocurve-based rendering for freeform surfaces
ACM Transactions on Graphics (TOG)
Comparison of surface and derivative evaluation methods for the rendering of NURB surfaces
ACM Transactions on Graphics (TOG)
Accelerated walkthrough of large spline models
Proceedings of the 1997 symposium on Interactive 3D graphics
Fast termination criterion for recursive subdivision of Bézier curves
ACM-SE 37 Proceedings of the 37th annual Southeast regional conference (CD-ROM)
Multiresolution rendering by sewing trimmed NURBS surfaces
Proceedings of the seventh ACM symposium on Solid modeling and applications
Interactive Display of Large NURBS Models
IEEE Transactions on Visualization and Computer Graphics
Budget sampling of parametric surface patches
I3D '03 Proceedings of the 2003 symposium on Interactive 3D graphics
Computational Methods for Geometric Processing. Applications to Industry
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
Incremental rendering of deformable trimmed NURBS surfaces
Proceedings of the ACM symposium on Virtual reality software and technology
GPU-based trimming and tessellation of NURBS and T-Spline surfaces
ACM SIGGRAPH 2005 Papers
Interactive high quality trimmed NURBS visualization using appearance preserving tessellation
VISSYM'04 Proceedings of the Sixth Joint Eurographics - IEEE TCVG conference on Visualization
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Trimmed non-uniform rational B-splines have become a very useful surface representation form in the mechanical CAD industry. Previous rendering methods use the de Boor algorithm to evaluate the surface at equal increments in parameter space. This yields polygons which are then rendered. Alternatively the Oslo algorithm and Boehm's knot insertion algorithms are used in a subdivision approach. In this paper a new method is presented for rendering trimmed NURB surfaces of arbitrary order using the adaptive forward differencing (AFD) technique. This method extends the AFD technique to higher order, efficiently computes the basis matrix for each span, calculates the shading approximation functions for rational surfaces, and trims and image maps NURB surfaces. Trimming is accomplished by using AFD to scan convert the trimming curves in parameter space, thus producing the intersection points between the trim curves and an isoparametric curve across the surface. A winding rule is used to determine the regions bounded by the curve which are then rendered with AFD. The method is suitable for both hardware and software implementations, however, higher order surfaces require very high precision due to the forward difference nature of the algorithm.